Rotate posed character around the Z axis without deformation
The problem is that you have moved the center of the mesh and the rig several times (while in edit and pose mode). This is a big no no and would have brought about even more problems if you had continued on to do more complex transforms/animation etc.



TL;DR: Clear all your object's transforms, and update the origin points for the rig and the model.



To fix.


Select the character and the rig and hit ShiftH to hide the rest of the scene so as to work without any distractions.
Select the character HaighMan and clear all transforms, Rotation AltR, Location AltG and Scale AltS.
Select the entire rig, which is currently in pose mode with A and repeat the previous steps for clearing all transforms.
Still selecting the rig, use CtrlTab to go to object mode and repeat the steps again for clearing transforms.

Providing you followed the steps above, your scene should now look something like this.


Select the rig and Tab into edit mode and adjust it to fit the model, select the root bone and use ShiftS > Cursor to Selected and then use CtrlShiftAltC > Origin to 3D Cursor. You can then select the rig in object mode and rotate the character 90° on the Y axis to have it stand upright.


All should be well now, it is fixed but still broken as your previous animation keyframes are still on the armature. I would highly recommend clearing these and animating it again and also re-applying the model to the armature. If you now hit play, it will jump to the keyframed location and the character will start walking, you are now also able to rotate and scale each bone without any weird deformations.


More reading:


Weird Armature Deformation
How do I apply a simple armature that I made to a model?
How can I automatically generate vertex groups for an armature?